The DOI matches its Crossref record; 56 of the 58 references it cites were found in a registry or an index.
Factors affecting the process of proficient mental addition and subtraction: case studies of flexible and inflexible computers
Open accessAbstract
The relationship between mental computation and number sense is complex: mental computation can facilitate number sense when students are encouraged to be flexible, but flexibility and number sense is neither sufficient nor necessary for accuracy in mental computation. It is possible for familiarity with a strategy to compensate for a lack of number sense and inefficient processes. This study reports on six case studies exploring Year 3 students’ procedures for and understanding of mental addition and subtraction, and understanding of number sense and other cognitive, metacognitive, and affective factors associated with mental computation. The case studies indicate that the mental computation process is composed of four stages in which cognitive, metacognitive and affective factors operate differently for flexible and inflexible computers. The authors propose a model in which the differences between computer types are seen in terms of the application of different knowledges in number facts, numeration, effect of operation on number, and beliefs and metacognition on strategy choice and strategy implementation.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“In the particular context of number equalities, we promoted this flexibility of thinking by directing students' attention to relations and restraining their computational tendency, rather than teaching them a set of strategies which have proven to have a negative impact on the development of flexibility in other contexts [32].”
From Third Grade Students’ Use of Relational Thinking (2021) · cites this paper as [32]
Experimental — accuracy not yet measured
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Handbook of research on mathematics teaching and learning
(1992) · Choice Reviews Online · doi:10.5860/choice.30-2122 · Cited by 6,126
Advances in Instructional Psychology
(2019) · Routledge eBooks · doi:10.4324/9781315864341 · Cited by 2,534
Research on Affect in Mathematics Education: A Reconceptualization
McLeod, D. B. (2006) · Emerald Group Publishing Limited eBooks · doi:10.1108/978-1-60752-874-620251028 · Cited by 1,224
The development of mathematical thinking
Ginsburg, H. P. (1983) · Academic Press eBooks · Cited by 967
Acquisition of mathematics concepts and processes
Lesh, R., & Landau, M. (1983) · Academic Press eBooks · Cited by 725
Dimensions of thinking and cognitive instruction
(1991) · Choice Reviews Online · doi:10.5860/choice.28-3406 · Cited by 631
Development of Children's Problem-Solving Ability in Arithmetic.
Riley, M. S. (1984) · Cited by 619
Dimensions of Thinking and Cognitive Instruction
Jones, B. F., & Idol, L. (2013) · Routledge eBooks · doi:10.4324/9780203771686 · Cited by 454
Promoting Access to Knowledge, Strategy, and Disposition in Students: A Research Synthesis
Prawat, R. S. (1989) · Review of Educational Research · doi:10.3102/00346543059001001 · Cited by 437
A Proposed Framework for Examining Basic Number Sense.
McIntosh, A. (1992) · for the learning of mathematics · Cited by 404
Research works printed but not linked: 3
- Heirdsfield, A. M., & Cooper. T. J. (1997). The architecture of mental addition and subtraction. Paper presented at the annual conference of the Australian Association of Research in Education, Brisbane, Australia. Retrieved on September 23, 2003 from http://www.aare.edu.au/97pap/heira395.htm
- Maier, 1977, Folk math, Instructor, 86, 84
- Sierink, 1991, Children's understanding of place value, Australian Journal of Early Childhood, 16, 33
Cited by
Brezovszky, B., McMullen, J. A., Veermans, K., Hannula‐Sormunen, M. M., Rodríguez-Aflecht, G., Pongsakdi, N., Laakkonen, E., & Lehtinen, E. (2018) · Computers & Education · doi:10.1016/j.compedu.2018.09.011 · Cited by 226
Acquisition and use of shortcut strategies by traditionally schooled children
Torbeyns, J., Smedt, B. D., Ghesquière, P., & Verschaffel, L. (2008) · Educational Studies in Mathematics · doi:10.1007/s10649-008-9155-z · Cited by 90
Efficiency and flexibility of indirect addition in the domain of multi-digit subtraction
Torbeyns, J., Ghesquière, P., & Verschaffel, L. (2008) · Learning and Instruction · doi:10.1016/j.learninstruc.2007.12.002 · Cited by 80
The Development of Children's Adaptive Expertise in the Number Domain 20 to 100
Torbeyns, J., Verschaffel, L., & Ghesquière, P. (2006) · Cognition and Instruction · doi:10.1207/s1532690xci2404_2 · Cited by 69
A Local Instruction Theory for the Development of Number Sense
Nickerson, S. D., & Whitacre, I. (2010) · Mathematical Thinking and Learning · doi:10.1080/10986061003689618 · Cited by 63
Metadata
- Authors
- Heirdsfield, A. M., & Cooper, T. J.
- Affiliations
- Queensland University of Technology (AU)
- Corresponding author
- Heirdsfield, Ann M.
- ORCID
- Heirdsfield, Ann M.
- Venue
- The Journal of Mathematical Behavior
- Publisher
- Elsevier BV
- Published
- 2004-01
- Volume
- 23
- Issue
- 4
- Pages
- 443-463
- ISSN
- 0732-3123 (ISSN-L)
- OpenAlex
- W2156159029
- Cited by
- 78
- References
- 58
- Citations by year
- 2026: 1 · 2025: 2 · 2024: 2 · 2023: 3 · 2022: 6 · 2021: 3 · 2020: 4 · 2019: 7 · 2018: 5 · 2017: 5 · 2016: 9 · 2015: 5 · 2014: 4 · 2013: 2 · 2012: 2
- FWCI
- 1.69
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- The Journal of Mathematical Behavior (publishedVersion)
- QUT ePrints (Queensland University of Technology) (submittedVersion)
- Topics
- Social Sciences › Psychology › Developmental and Educational Psychology › Cognitive and developmental aspects of mathematical skills
- Social Sciences › Education › Mathematics Education and Pedagogy
- Social Sciences › Education › Mathematics Education and Teaching Techniques
- Keywords
- mental arithmetic, mental addition, number sense, strategy selection, metacognition, emotional factors, number facts, numeration, strategy implementation
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
